Generating sounds

A sound can be represented mathematically by a sine wave, with a certain amplitude, frequency, and phase. We can randomly select frequencies from a list specified on Wikipedia at http://en.wikipedia.org/wiki/Piano_key_frequencies that complies with the following formula:

The variable n in this formula is the number of the piano key. We will number the keys from 1 to 88. We will also select the amplitude, duration, and phase at random.

How to do it...

We will begin by initializing random values, then generate sine waves, compose a melody, and finally, plot the generated audio data with Matplotlib.

1. Initialization.

   Initialize to random values:

   • the amplitude between 200 to 2000,

   • the duration to 0.01 to 0.2,

   • the frequencies using the formula already mentioned

   • the phase to values between 0 and 2 pi

   • NTONES = int(sys.argv[1])

     amps = 2000. * numpy.random.random((NTONES,)) + 200.
     durations = 0.19 * numpy.random.random((NTONES,)) + 0.01
     keys = numpy.random.random_integers(1, 88, NTONES)
     freqs...